Today, I am here to share with you results from our new report, Algebra I and Geometry
Curricula: Results from the 2005 High School Transcript Mathematics Curriculum Study.
This is the first study from the National Center for Education Statistics (NCES)
to explore the content and level of challenge of high school algebra I and geometry
courses in public schools across the Nation. The study uses data from the National
Assessment of Educational Progress (NAEP) High School Transcript Study and the NAEP
mathematics assessment.

There are several reasons why we undertook this study. The data we have collected
in the High School Transcript Study over the years have shown a steady increase
in numbers of mathematics courses that high school graduates have completed. Not
only are graduates taking more courses, but they are also taking more high-level
courses. This is true for White, Black, and Hispanic graduates. However, there has
not been a comparable increase in the NAEP twelfth-grade mathematics scores over
the same period, and the achievement gaps separating Black and Hispanic graduates
from White graduates have not changed much. Therefore, we wanted to know the actual
content of the courses graduates were taking, and if there might be a disparity
in course content observable for White versus Black or Hispanic graduates.

The Mathematics Curriculum Study explores the content and challenge of algebra I
and geometry courses taught in high school. The study was conducted as part of the
2005 NAEP High School Transcript Study. It was based on a nationally representative
sample of 17,800 public high school graduates, representing a population of about
2 million graduates. The graduates in the sample were in 550 high schools around
the country. The study incorporated the transcripts and NAEP mathematics scores
of these graduates, along with over 120 algebra I, geometry, and integrated mathematics
textbooks used by their schools. While these textbooks were being used in 2005,
the data we obtained from them is still relevant. In 2009, the most recent High
School Transcript Study, we examined lists of the textbooks schools were using in
that year and found very few differences, compared to the books in use in 2005.

The participating schools provided titles of the textbooks they used in their mathematics
courses, and the teachers indicated what chapters they intended to cover in their
courses. The review questions at the end of each chapter in the textbooks collected
were coded for content and challenge, using a coding system first developed for
the Trends in International Mathematics and Science Study. The textbook data was
summarized at the student level to provide the results for the study.

Six broad curriculum topics for the materials covered in algebra I and geometry
courses were identified in the study. These broad topics refer to the mathematics
content areas that graduates covered in their courses, including elementary and
middle school mathematics, introductory and advanced algebra, two-dimensional and
advanced geometry, and other high school mathematics, which refers to topics traditionally
taught after algebra II, such as trigonometry and pre-calculus. The algebra I and
geometry courses taken by the graduates were also grouped in three course levels—Beginner,
Intermediate, and Rigorous—according to the topics and the degree of challenge
of the textbooks used in the courses.

The study has some limitations. First, its coverage is restricted to public high
school graduates who obtained a regular or honors diploma and who completed either
algebra I or a geometry course in high school. Graduates who took algebra I before
high school were not included in the algebra I results, while graduates who took
geometry before high school were not included in the geometry results. Second, because
the population of focus is graduates, dropouts are not included in the results.
Third, the textbooks served as a measure of the intended curriculum for algebra
I and geometry courses. The study could not measure how well the course curriculum
was implemented in the classroom. Fourth, the study cannot identify cause and effect
relationships between courses and student performance.

All of the study results reported today are based on samples, which means that there
is a margin of error associated with each score or percentage. Therefore, in the
report we only identify those differences in scores or percentages that meet our
standard for statistical significance.

Algebra I Results
On average, the nation’s algebra I courses devoted about two-thirds of their
content to algebra, with about 37 percent to introductory algebra and 28 percent
to advanced algebra. About 13 percent of the content of the average algebra I course
was elementary and middle school mathematics, while nearly a quarter was devoted
to geometry or other high school mathematics.

Rigorous courses devoted about 10 percent of their content to elementary and middle
school mathematics. Both the beginner and intermediate courses devoted more of their
content to this topic. Conversely, rigorous algebra I courses devoted 16 percent
of their content to other high school mathematics, more than either beginner or
intermediate courses. Regardless of course level, algebra I courses devoted between
62 and 67 percent of their content to introductory and advanced algebra topics,
with rigorous courses putting more emphasis on advanced algebra topics than either
beginner or intermediate courses.

Few racial/ethnic differences were found among graduates by the algebra I course
level. About 24 percent of Asian/Pacific Islander graduates and 19 percent of Hispanic
graduates took beginner algebra I courses, which were higher than the 12 percent
of White graduates taking such courses. Two factors should be kept in mind when
considering these higher percentages. First, the study looked at high school graduates,
not all twelfth-grade students. In 2005, the high school drop-out rate for Hispanics
was 22 percent, compared to 10 percent for Blacks, 6 percent for Whites, and 3 percent
for Asian/Pacific Islanders. Second, there were differences in the percentages of
graduates who took algebra I before entering high school across race/ethnicity.
In 2005, 30 percent of Asian/Pacific Islander graduates took algebra I before entering
high school, compared to 23 percent of Whites, 8 percent of Blacks and 10 percent
of Hispanics. These students were not part of the algebra I results in the study.

High schools typically designated the algebra I classes they offer as two-year,
regular, and honors classes. In the study, we compared the course levels we developed
to the school course descriptions. Regardless of the school designation, most graduates
in algebra I courses had an intermediate level course. The study found that graduates
in regular algebra I classes were more likely to receive a course ranked as a rigorous
level course than graduates in honors algebra I classes. Only 18 percent of the
graduates in honors algebra I classes had a rigorous level course, compared to 34
percent of graduates in regular algebra I classes.

Geometry Results
When looking at the nation’s geometry courses, about two-thirds of the coverage
was devoted to two-dimensional and advanced geometry. Around 42 percent of the content
focused on two-dimensional geometry, while 24 percent focused on advanced geometry.
About 13 percent was devoted to elementary and middle school mathematics, while
21 percent covered algebra and other high school mathematics.

Beginner geometry courses devoted 14 percent of their content to elementary and
middle school mathematics, which was more than either intermediate or rigorous geometry
courses. Rigorous geometry courses devoted more coverage to both two-dimensional
and advanced geometry than either beginner or intermediate courses.

About 67 percent of graduates had a geometry course ranked as intermediate. Around
21 percent of the graduates had a rigorous level geometry course, while 12 percent
had a beginner level course. When the data are broken down by race/ethnicity, the
distributions for Black, Hispanic, and Asian/Pacific Islander graduates showed similar
proportions to White graduates.

Geometry classes offered by high schools were typically titled as informal, regular,
and honors classes. Regardless of the school course title, most high school graduates
received a course ranked as an intermediate level geometry course.
About 54 percent of graduates in informal geometry classes, 68 percent of graduates
in regular geometry classes, and 62 percent of graduates in honors geometry classes
were in courses ranked as intermediate level. Graduates in honors geometry classes
were less likely to receive a beginner level course and more likely to receive a
rigorous level course than graduates in either informal or regular geometry classes.

NAEP Performance
When looking at the performance of graduates on the NAEP twelfth-grade mathematics
assessment, graduates in rigorous algebra I and geometry courses scored higher on
NAEP. Graduates in rigorous algebra I courses had a mean NAEP algebra score of 146,
compared to 137 for graduates in beginner courses. Graduates in rigorous geometry
courses had a mean NAEP geometry score of 159, which was higher than the scores
for graduates in beginner or intermediate geometry courses. White graduates had
higher NAEP algebra and geometry scores than either Black or Hispanic graduates,
regardless of the level of the algebra I or geometry course.